Transcript Modelling Fission Product Effects in UO2
Predicting the Effect of Fission Products in UO
2 Presentation at the VERCORS meeting Kaajal H. Desai a , David Parfitt a , Scott L. Owens b , Robin W. Grimes a a Department of Materials, Imperial College, Prince Consort Road, London, UK b Nexia Solutions, Hinton House, Risley, Warrington, Chesire UK Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE
Aim:
demonstrate what atomic scale computer simulation developing can a provide, better that is useful understanding of for the behaviour of nuclear fuels (particularly as they relate to fission product behaviour).
What can simulations do for you?
• Correlate experimental data with existing physical models (fill in the gaps and work out what’s missing).
• Generate data for known physical processes (point the way to better hunting grounds for experimental work).
• Develop new physical models that underpin phenomena (work out what science actually matters).
First – Correlate experimental data with physical models
• Use fission product inventories to investigate fuel swelling.
• Lattice swelling/contraction due to accommodation of soluble fission products as a function of fission product concentration.
• Affect on mechanical properties – elastic constants and bulk moduli as a function of fission product concentration.
First – Correlate experimental data with physical models
• The Physical process is well established.
• No new “science” is being suggested.
• Checking existing data and correlating it.
• Hence: fillng in the gaps and working out what’s missing.
Swelling Calculation
Defect volume,
V D
, is calculated by:
K T V 0
(Å 3
V D
K
(Å 3 ) initial unit cell volume
T V
0
df dV
T
eV -1 ) is the isothermal compressibility,
f
(eV) the internal defect formation energy calculated within the Mott-Littleton approximation Mechanical constants are calculated using:
K T
c
11 3 2
c
12 Bulk Modulus
B
1
K T
Model Considerations
Range of Fission Products (FP) Different solution sites – U and O substitution, interstitial octahedral site, cluster sites Fuel Stoichiometry Zr 4+ , Ce 4+ - sites: ,
U Ce U X
Sr 2+ - sites : Isolated Clustered
Sr U
''
U
V
2
U O
U
Sr U
''
Sr U
'' : :
V O
U U
X
'
U
U
Sr U
'' : 2
U U
X
Y 3+ , La 3+ , Pr 3+ , Nd 3+ , Sm 3+ , Eu 3+ , Gd 3+ , Dy 3+ 2
La
'
U
V
O
La
'
U
U
U
La U
'
La U
' : :
V O
U
U
X
La U
' 2
La U
' sites: :
V O
X
Results I: Zr accommodation
Results II: Ce accommodation
FP Accommodation: Sr
Number of ways Sr can be accommodated in lattice UO 2 - substitution on U site is energetically favoured Charge compensated in 2 ways V O ·· Oxygen vacancy formation Uranium oxidation, U 5+ U U · formation Similarly for the trivalent, Y and lanthanide fission products
Results III: Sr accommodation
Results IV: La accommodation
Results V: Pr accommodation
Results VI: Nd accommodation
Results VII: Sm accommodation
Results VIII: Eu accommodation
Results IX: Gd accommodation
Results X: Dy accommodation
Results XI: Predicted Change in Bulk Modulus due to Sr
Results XIII: Predicted Change in Bulk Modulus due to Zr and Ce
Summary
A specific burnup yields a specific fission product inventory. This work aims to provide data from which it is possible to determine a change of lattice parameter or change in mechanical property of the UO 2 lattice as a consequence of the dissolved fraction of those fission products. For example, Sr 2+ --> Increased lattice parameter Zr 4+ --> Decreased lattice parameter
Second – Generate data for known physical processes
• The aim is to help to direct experimental work.
• The physical process is well established, but the significance to fuels not necessarily realised.
• Appropriate experimental data does not yet exist.
• Classic example: compositional changes due to segregation.
Aim of Segregation Study
•
Computer simulation is used to investigate the accommodation and segregation of fission products to the (111), (110) and (100) surfaces of UO 2 Fission products considered: Ce 4+ , Zr 4+ , Ba 2+ , Sr 2+ , Kr 0 and Xe 0 Ba 2+ vacancy and Sr 2+ Kr 0 and Xe 0 are charge compensated by a single oxygen are compensated by two oxygen vacancies • Important results concern: Segregation dependence on the surface type Defect cluster orientation with respect to a given surface Anion termination configuration for dipolar surfaces • This work provides information regarding the anisotropic release of fission products.
Methodology
• Computational codes CASCADE and MARVIN are used.
• A defect (isolated or clustered) is introduced to a characteristic lattice and moved stepwise through the bulk.
• The total energy of Region 1 is calculated for each step and the energies are compared with respect to when the cluster is furthest from the surface (i.e. in the bulk).
Divalent ClusterConfigurations: (111) • The nearest neighbour {(Ba/Sr U )’’:(V O ) ..
} configuration is preferred.
• There are four unique nearest neighbour cluster configurations with respect to the (111) surface, shown below.
• Each of these configurations must be modelled.
Ce 4+ and Zr 4+ (111) Segregation • The Zr 4+ segregation energy, E S = 0.26eV, the trap energy, E T = 0.35eV, which suggests that Zr 4+ remain trapped just beneath the (111) surface.
• For Ce 4+ , E S = 0.23eV, which suggests that Ce 4+ does not segregate to the (111) surface.
• (E T - E S ) is negligible, which suggests that the trapping observed with Zr 4+ is not present.
Ba 2+ and Sr 2+ (111) Segregation • The segregation energy E S 2.71eV for Ba 2+ , thus Ba 2+ = will segregate to the (111) surface.
• A similar trend is observed for Sr 2+ , where E S = -1.60eV, though the driving force is reduced.
• In the bulk ( 10 Å) there is little cluster configuration preference.
• Near to the surface, there is a dependence on defect cluster configuration.
Ce 4+ and Zr 4+ (110) Segregation • The Zr 4+ segregation energy, E S Zr 4+ = 0.14eV, which suggests that will not segregate to the (110) surface.
• The nonlinear change in energy is due to alternating compression and dilation of atomic layers.
• For Ce 4+ E S suggests that = 0.67eV which Ce 4+ does not segregate to the (110) surface, more strongly than Zr 4+ .
• The trend for Ce 4+ and Zr 4+ not segregating to the (110) surface is similar to the trend observed for the (111).
Ba 2+ and Sr 2+ (110) Segregation • The Ba 2+ , segregation energy, E S = -2.84eV, suggests that Ba segregate to the (110) surface.
2+ will • A similar trend is observed for Sr 2+ where E S = -1.67eV; clearly the driving force is reduced.
• The segregation of Ba 2+ and Sr 2+ is very similar to that observed with the (111); similar segregation energies and cluster dependence nearer to the surface.
Conclusions Concerning Segregation • Computer simulation calculations suggest that Ce 4+ and Zr 4+ show no tendency to segregate to the (111) or (110) surfaces of UO 2 .
• Zr 4+ demonstrates a tendency to segregate to the (100)A surface, which suggests segregation is a function of surface.
• Ba 2+ and Sr 2+ display a tendency to segregate to the (111) and (110) surfaces, with cluster configuration becoming important near the surface in both cases.
• Segregation is not only a function of fission product chemistry and surface, but also cluster configuration with respect to surface and anion termination in the case of Type 3 surfaces.
• Fission product release will be highly anisotropic.
Third – identify new physical processes
Aims of the study
Develop a robust computational model that can simulate UO 2 and fission gasses. It must replicate: High temperature behaviour and defect energies Good core-core repulsion for high energy collisions Apply this model to predict the evolution of bubbles with respect to: Bubble size Fission gas pressure Temperature of material Recoil energy
All micrographs courtesy of Ian Ray ITU Transgranular fracture showing aligned metal particles leading to a grain boundary Transgranular fracture showing internal void, smaller gas bubbles and larger bubbles at grain boundaries
Intergranular and Transgranular Fracture
Molecular dynamics of radiation enhanced helium re-solution
Helium in bubbles can return to the crystal lattice via radiation-enhanced re-solution rather than thermal resolution ...
But how does this actually work in practice?
It is thought that high-energy fission fragments 'knock out' helium atoms from bubbles leading to resolution.
What Bubbles?
Several different bubble sizes and shapes have been investigated: Octahedra constructed from (111) surfaces Infinite pores from (110) surfaces Spheres Larger 'infinite' slab surfaces In UO 2 the morphology of the bubbles is roughly spherical but (111) surfaces are observed (which also dominate equilibrium voids).
MD Simulation of 5 keV U <111> Recoil
Event sequence:
• Ballistic phase.
• Thermal spike.
• Displacement damage interacts with the He bubble disrupting the bubble/lattice interface.
• Beginning of recovery phase.
MD Simulation of 5 keV U <111> Recoil
Event sequence:
• Ballistic phase and thermal spike are not seen.
• Displaced lattice ions interacts with the He bubble disrupting the bubble/lattice interface.
• He “leaks” into the damaged (partly disordered) lattice.
MD Simulation of 5 keV U <111> Recoil
Event sequence:
• Ballistic phase.
• Thermal spike.
• Lattice ions are displaced into the bubble.
• UO 2 units are relocated across the bubble facilitating the overall movement of the bubble.
Why is this exciting?
• Physics behind this mode of radiation enhanced resolution is fundamentally different to what has been proposed previously.
• May explain some 'anomalous' terms in bubble migration models.
• More accurate and confident modelling leads to less conservatism in fuel performance codes.
Directions of Further Work
• • • • Long timescale dynamics of bubble migration.
He migration along dislocations.
'Phase diagram' of the bubbles as a function of temperature, He pressure and displacement cascade energy.
Examine Xe gas behaviour as well – Xe adopts solid structures in fission gas bubbles. • Aim to aid in reducing conservatism.
Summary
Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE • A simple computational model has been used to generate structure (and defect structure) property composition relationships.
• Correlated experimental data with physical models (filled in some gaps and work out what’s missing).
• Identified computational variations close to surfaces (pointed the way for experimental investigations).
• Developed new physical models that underpin phenomena (worked out what bit actually matters).
• Need to use a range of computational techniques to underpin and generate the defect property relationships.